The moral influence theory is described here: Moral influence theory of atonement - Wikipedia . There are four or five theories of atonement in Christianity. Dawkins is representing things as if there were only one: the one it is easiest to object to, of course.
There is a theory promoted by the Franciscans that Jesus was not an afterthought or a 'scapegoat' but first thought, God in solidarity with his creation, and Jesus being the reason for creation.
From this perspective, God is appreciated with a different emphasis. God is not an angry or vindictive God, demanding the suffering and death of Jesus as a payment for past sin. God is, instead, a gracious God, sharing divine life and love in creation.
Another great philosopher and theologian, Franciscan John Duns Scotus (1266-1308), proclaimed and defended the primacy of the Incarnation. He based his view on the Scriptures and early theologians and on logic. He argued, for example, that God's supreme work, the Incarnation, had to be first and foremost in God's mind. It could not be dependent on or occasioned by any action of humans, especially sin.
As for Dawkins all too many people who claim a high level of knowledge in the field of science have little knowledge in Biblical faith beyond that of a child which explains why Dawkins knows he is out of his league when it comes to the science of philosophy or theology beyond fundamentalism.